Optimal Ground-State Preparation with a Guiding State
Abstract
Suppose a Hamiltonian H has a unique ground state |ψ0⟩ with an eigenvalue E0, and we have an estimate Ẽ0 such that |Ẽ0−E0|≤δ, and there is a gap of at least 3δ between E0 and all other eigenvalues. Suppose we have a unitary A available that can produce a "guiding state'" A|0⟩ that has overlap at least γ with |ψ0⟩. We show how to obtain an η-approximation of |ψ0⟩ with probability at least 1−ε using O(log(1/ε)/γδ+ log(1/η)/δ) applications of U=eiH its inverse, and O(log(1/ε)/γ) applications of A and its inverse. We give two different algorithms, one based on interleaving amplitude amplification and error-reduction in the style of [HMdW03], and one using the composition of transducers. This paper is the state-preparation follow-up to our two recent ground-state-energy estimation papers [JW26,SdW26]. Combined with the optimal energy-estimation of [JW26], our results show the claimed upper bound for ground-state preparation. The bound is optimal up to a constant factor in terms of the number of applications of U and U† if ε=η, as follows from [SdW26]. In one of our approaches to ground state preparation, we construct transducers for amplitude amplification and LCU that might be of independent interest.
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BibTeX
@misc{jeffery2026optimal,
title = {{Optimal Ground-State Preparation with a Guiding State}},
author = {Stacey Jeffery and Rolando D. Somma and Freek Witteveen and Ronald de Wolf},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.38091},
eprint = {2609.38091},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38091},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Optimal Ground-State Preparation with a Guiding State
AU - Stacey Jeffery
AU - Rolando D. Somma
AU - Freek Witteveen
AU - Ronald de Wolf
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2609.38091
UR - https://arxiv.org/abs/2609.38091
AB - Suppose a Hamiltonian H has a unique ground state |ψ_0⟩ with an eigenvalue E_0, and we have an estimate Ẽ_0 such that |Ẽ_0−E_0|≤δ, and there is a gap of at least 3δ between E_0 and all other eigenvalues. Suppose we have a unitary A available that can produce a "guiding state'" A|0⟩ that has overlap at least γ with |ψ_0⟩. We show how to obtain an η-approximation of |ψ_0⟩ with probability at least 1−ε using O(log(1/ε)/γδ+ log(1/η)/δ) applications of U=e^iH its inverse, and O(log(1/ε)/γ) applications of A and its inverse. We give two different algorithms, one based on interleaving amplitude amplification and error-reduction in the style of [HMdW03], and one using the composition of transducers. This paper is the state-preparation follow-up to our two recent ground-state-energy estimation papers [JW26,SdW26]. Combined with the optimal energy-estimation of [JW26], our results show the claimed upper bound for ground-state preparation. The bound is optimal up to a constant factor in terms of the number of applications of U and U^† if ε=η, as follows from [SdW26]. In one of our approaches to ground state preparation, we construct transducers for amplitude amplification and LCU that might be of independent interest.
ER -